Matching Logic

Abstract

This paper presents matching logic, a first-order logic (FOL) variant forspecifying and reasoning about structure by means of patterns and patternmatching. Its sentences, the patterns, are constructed using variables,symbols, connectives and quantifiers, but no difference is made betweenfunction and predicate symbols. In models, a pattern evaluates into a power-setdomain (the set of values that match it), in contrast to FOL where functionsand predicates map into a regular domain. Matching logic uniformly generalizesseveral logical frameworks important for program analysis, such as:propositional logic, algebraic specification, FOL with equality, modal logic,and separation logic. Patterns can specify separation requirements at any levelin any program configuration, not only in the heaps or stores, without anyspecial logical constructs for that: the very nature of pattern matching isthat if two structures are matched as part of a pattern, then they can only bespatially separated. Like FOL, matching logic can also be translated into purepredicate logic with equality, at the same time admitting its own sound andcomplete proof system. A practical aspect of matching logic is that FOLreasoning with equality remains sound, so off-the-shelf provers and SMT solverscan be used for matching logic reasoning. Matching logic is particularlywell-suited for reasoning about programs in programming languages that have anoperational semantics, but it is not limited to this